I encourage you to look twice at your question - I believe that, under close scrutiny, you will see that it contains its own answer.
No one is advocating for prohibiting people from peacefully expressing their genuinely-held political beliefs in ways that do not infringe on the rights of others in public (unless you want to count the multitudes of minority voters who are regularly removed from voting rolls by GOP lawmakers or subjected to onerous identification requirements and other intimidation tactics...). If a person's "genuinely-held political beliefs" involve racism, sexism, homophobia, etc., and if said person "genuinely believes" that the appropriate way to exert their opinion upon society is to discriminate against the people they hate or even inflict violence upon them, then they are crossing a line established by our societal norms and threatening the stability of society itself.
If a person's genuinely held political beliefs lead them to enact discrimination or violence upon others then they have placed themselves outside of society and are by definition not valid input sources for determining societal norms and laws.
Are you aware of anyone in this thread, or of any major national movement, advocating for a tolerance-based right to perform sexual acts in public in front of children? Looking past the strange and extreme strawman you've propped up, the reasons for tolerance in society are multitudinous. It prevents misunderstanding, fear, and hatred from festering and potentially giving rise to violence.
As a simple thought experiment ask yourself the following question. How many individuals hailing from tolerant communities or organizations have you seen commit mass shootings? Contrast that to the number of individuals committing public violence who hold intolerance as a virtue. Public violence is a serious negative for everyone and its prevention should be reason enough to support tolerance as a basic tenet of societal health. The fact of the matter, no matter who might dislike it, is that modern societies are, for the most part, very diverse. Without tolerance for differences violence is a forgone conclusion in the modern world.
This type of behavior is exactly why I block all online ads, always. The fact that large companies like Google and Facebook (and many others) not only go out of their way to deceive their users about what they actually do with their data, but actually actively lobby relevant governments to prevent any kind of privacy protections from being enacted, is all the evidence I need to understand that their operations are fundamentally at odds with the concept of personal privacy and freedom.
There is an argument that is often made when I (or others) advocate for ad blocking, and it always involves the evocation of "the little guy" content creator / website owner who gets shafted when adblockers are used. The problem with this argument, and the reason that I feel fully justified - even obligated - to blanket block all ads, is that it is essential to exert SOME kind of pressure against the large surveillance companies. They clearly don't care about their user's preferences, so the next way to fight this trend is to erode, to the greatest extent possible, the economics of their operations.
Facebook and the rest of the surveillance corporations can create shadow profiles on me from my digital crumbs if they want. At the end of the day I cannot stop them from doing that - and that's why I will never view, click on, or interact with any online ad under any circumstances, to ensure that they don't reap any significant economic reward from stalking me. When / if a semblance of sanity returns to online advertising and the personal privacy rights of users are respected by default, I will change my behavior accordingly so that content creators are supported. In the mean time I directly donate where possible.
On a side note, I notice an obliquely similar situation with Comcast and other big, anti-consumer tech companies that cannot avoid having large customer-facing communications divisions. The people they have manning their phone systems are inevitably exhausted, desperate-sounding, and clearly under some sort of sales quota. Sometimes I almost think that Comcast intentionally makes the lives of their call center employees as miserable as possible so that customers feel guilty dealing with them on the phone and have a lower probability of complaining about the company - after all, why beat up the peon in the cubicle farm about working for a company they already hate? It's almost as if these big companies have decided to use regular people's lives as human shields to hide their inhumanity behind.
No one is advocating for prohibiting people from peacefully expressing their genuinely-held political beliefs in ways that do not infringe on the rights of others in public (unless you want to count the multitudes of minority voters who are regularly removed from voting rolls by GOP lawmakers or subjected to onerous identification requirements and other intimidation tactics...). If a person's "genuinely-held political beliefs" involve racism, sexism, homophobia, etc., and if said person "genuinely believes" that the appropriate way to exert their opinion upon society is to discriminate against the people they hate or even inflict violence upon them, then they are crossing a line established by our societal norms and threatening the stability of society itself.
If a person's genuinely held political beliefs lead them to enact discrimination or violence upon others then they have placed themselves outside of society and are by definition not valid input sources for determining societal norms and laws.